formal language derivations

Logic/Language/M.hs

@@ -1,62 +0,0 @@
-module Logic.Language.M where
-
-import Logic.Language (Language(..), Seq(..))
-
--- The language M
--- (from "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter)
-data AlphaM
-  = M
-  | I
-  | U
-  deriving (Eq, Show)
-
-type StringM = [AlphaM]
-
-instance Language AlphaM where
-  isWellFormed (M:_) = True
-  isWellFormed _ = False
-
-  axiom0 = [[M, I]]
-  infer1 =
-    [ mRule1
-    , mRule2
-    , mRule3
-    , mRule4
-    ]
-
--- RULE I: If you possess a string whose last letter is I, you can add on a U at the end.
-mRule1 :: StringM -> [StringM]
-mRule1 [I] = [[I, U]]
-mRule1 (x:xs) = (x:) <$> mRule1 xs
-mRule1 _ = []
-
--- RULE II: Suppose you have Mx. Then you may add Mxx to your collection.
-mRule2 :: StringM -> [StringM]
-mRule2 string@(M:xs) = [string ++ xs]
-mRule2 _ = []
-
--- RULE III: If III occurs in one of the strings in your collection, you may
--- make a new string with U in place of III.
-mRule3 :: StringM -> [StringM]
-mRule3 string@(M:xs) = (M:) <$> aux xs
-  where
-    aux (x@I:xs@(I:I:xs')) = (U:xs'):((x:) <$> aux xs)
-    aux (x:xs) = (x:) <$> aux xs
-    aux _  = []
-mRule3 _ = []
-
--- RULE IV: If UU occurs inside one of your strings, you can drop it.
-mRule4 :: StringM -> [StringM]
-mRule4 string@(M:xs) = (M:) <$> aux xs
-  where
-    aux (x@U:xs@(U:xs')) = xs':((x:) <$> aux xs)
-    aux (x:xs) = (x:) <$> aux xs
-    aux _ = []
-mRule4 _ = []
-
-{-
-ghci> map Seq infer0 :: [Seq AlphaM]
-[MI]
-ghci> map Seq $ concat $ map ($ [M, I, I, I, I, U, U, I]) infer1
-[MIIIIUUIU,MIIIIUUIIIIIUUI,MUIUUI,MIUUUI,MIIIII]
--}